The set of nonlinear equations describing the standard model kinematics of the top quark antiquark production system in the dilepton decay channel has at most a fourfold ambiguity due to two not fully reconstructed neutrinos. Its most precise solution is of major importance for measurements of top quark properties like the top quark mass and $t\overline{t}$ spin correlations. Simple algebraic operations allow one to transform the nonlinear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be analytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree 16. The number of its real solutions is determined analytically by means of Sturm’s theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the polynomial in a given interval through binary bracketing.

We present a quenched lattice calculation of low energy constants using the chirally improved Dirac operator. Several lattice sizes at different lattice spacings are studied. We systematically compare various methods for computing these quantities, using pseudoscalar and axial vector correlators. We find consistent results for the different approaches, giving rise to $f_{\pi }=96(2)(4)\mathrm{MeV}$, $f_K=106(1)(8)\mathrm{MeV}$, $f_K/f_{\pi }=1.11(1)(2)$, $\Sigma =-(286(4)(31)\mathrm{MeV}{)}^3$, the average light quark mass $\overline{m}=4.1(2.4)\mathrm{MeV}$, and $m_s=101(8)\mathrm{MeV}$.

We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power-divergent additive renormalization of the topological susceptibility is calculated to 3 loops. Our work serves also as a test case of the techniques and limitations of lattice perturbation theory, it being the first 3-loop computation in the literature involving overlap fermions.

I demonstrate that the correlated angular distributions of final-state particles in both single-top-quark production and the dominant $Wjj$ backgrounds can be reliably predicted. Using these fully correlated angular distributions, I propose a set of cuts that can improve the single-top-quark discovery significance by 25%, and the signal to background ratio by a factor of 3 with very little theoretical uncertainty. Up to a subtlety in $t$-channel single-top-quark production, leading-order matrix elements are shown to be sufficient to reproduce the next-to-leading order correlated distributions.

In charmless nonleptonic $B$ decays to $\pi \pi$ or $\rho \rho$, the “color allowed” and “color suppressed” tree amplitudes can be studied in a systematic expansion in ${\alpha }_s(m_b)$ and ${\Lambda }_{\mathrm{QCD}}/m_b$. At leading order in this expansion their relative strong phase vanishes. The implications of this prediction are obscured by penguin contributions. We propose to use this prediction to test the relative importance of the various penguin amplitudes using experimental data. The present $B\to \pi \pi$ data suggest that there are large corrections to the heavy quark limit, which can be due to power corrections to the tree amplitudes, large up-penguin amplitude, or enhanced weak annihilation. Because the penguin contributions are smaller, the heavy quark limit is more consistent with the $B\to \rho \rho$ data, and its implications may become important for the extraction of $\alpha$ from this mode in the future.

We demonstrate a fully self-consistent microscopic realization of a kaon-condensed color-flavor locked state (${\mathrm{CFLK}}^0$) within the context of a mean-field Nambu–Jona-Lasinio (NJL) model at high density. The properties of this state are shown to be consistent with the QCD low-energy effective theory once the proper gauge neutrality conditions are satisfied, and a simple matching procedure is used to compute the pion decay constant, which agrees with the perturbative QCD result. The NJL model is used to compare the energies of the ${\mathrm{CFLK}}^0$ state to the parity even CFL state, and to determine locations of the metal/insulator transition to a phase with gapless fermionic excitations in the presence of a nonzero hypercharge chemical potential and a nonzero strange quark mass. The transition points are compared with results derived previously via effective theories and with partially self-consistent NJL calculations. We find that the qualitative physics does not change, but that the transitions are slightly lower.

Strangeness-changing decays of $B$ mesons to three-body final states of pions and kaons are studied, assuming that they are dominated by a $\Delta I=0$ penguin amplitude with flavor structure $\overline{b}\to \overline{s}$. Numerous isospin relations for $B\to K\pi \pi$ and for underlying quasi-two-body decays are compared successfully with experiment, in some cases resolving ambiguities in fitting resonance parameters. The only exception is a somewhat small branching ratio noted in $B^0\to K^{*0}{\pi }^0$, interpreted in terms of destructive interference between a penguin amplitude and an enhanced electroweak penguin contribution. Relations for $B$ decays into three kaons are derived in terms of final states involving $K_S$ or $K_L$, assuming that $\varphi K$-subtracted decay amplitudes are symmetric in $K$ and $\overline{K}$, as has been observed experimentally. Rates due to nonresonant backgrounds are studied using a simple model, which may reduce discrete ambiguities in Dalitz plot analyses.

Recent experiments at RHIC and theoretical considerations indicate that the quark-gluon plasma, present in the fireball of relativistic heavy-ion collisions, might be in a liquid phase. The liquid state can be identified by characteristic correlation and structure functions. Here definitions of the structure functions and pair correlations of the quark-gluon plasma are presented as well as perturbative results. These definitions might be useful for verifying the quark-gluon-plasma liquid in QCD lattice calculations.

If the neutrinos are Majorana fermions, there are at least three new, potentially observable $CP$-odd phases that parametrize $CP$-invariance violating phenomena. We currently have no information regarding any of them and know that two out of the three, the so-called Majorana phases, are very hard to access experimentally. Here, we discuss the effect of Majorana phases on charged-lepton electric dipole moments (EDM), and explicitly show that neutrino Majorana phases induce EDMs even in the absence of other sources of $CP$-invariance violation. We also argue that while the Majorana neutrino contribution to EDMs is tiny, there is one generic ultraviolet completion to the standard model plus massive Majorana neutrinos—the standard model plus a triplet Higgs boson—that leads to significantly enhanced contributions which are still proportional to the low-energy neutrino Majorana phases. If this particular scenario is realized in nature, it seems possible, at least in principle, to measure the Majorana phases by precisely measuring charged-lepton EDMs.

We present an improved measurement of the branching fraction for the electroweak penguin process $B\to X_s{\ell }^{+}{\ell }^{-}$, where $\ell$ is an electron or a muon and $X_s$ is a hadronic system containing an $s$-quark. The measurement is based on a sample of $152\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ events collected with the Belle detector at the KEKB energy asymmetric $e^{+}{e}^{-}$ collider. The $X_s$ hadronic system is reconstructed from one $K^{\pm }$ or $K_{\mathrm{S}}^0$ and up to four pions, where at most one pion can be neutral. Averaging over both lepton flavors, the inclusive branching fraction is measured to be $\mathcal{B}(B\to X_s{\ell }^{+}{\ell }^{-})=(4.11\pm 0.83(\mathrm{stat}{)}_{-0.81}^{+0.85}(\mathrm{syst}))\times {10}^{-6}$ for $M_{{\ell }^{+}{\ell }^{-}}>0.2\mathrm{GeV}/c^2$.

We identify and analyze quasiperiodic and chaotic motion patterns in the time evolution of a classical, non-Abelian Bogomol’nyi-Prasad-Sommerfield (BPS) dyon pair at low energies. This system is amenable to the geodesic approximation which restricts the underlying SU(2) Yang-Mills-Higgs dynamics to an eight-dimensional phase space. We numerically calculate a representative set of long-time solutions to the corresponding Hamilton equations and analyze quasiperiodic and chaotic phase space regions by means of Poincaré surfaces of section, high-resolution power spectra and Lyapunov exponents. Our results provide clear evidence for both quasiperiodic and chaotic behavior and characterize it quantitatively. Indications for intermittency are also discussed.

Realistic modeling of radiation transfer in and from variable accretion disks around black holes requires the solution of the problem: find the constants of motion and equation of motion of a lightlike geodesic connecting two arbitrary points in space. Here we give the complete solution of this problem in the Schwarzschild spacetime.

We investigate moduli stabilization in string gas compactification. We first present numerical evidence showing the stability of the radion and the dilaton. To understand this numerical result, we construct the 4-dimensional effective action by taking into account T-duality. It turns out that the dilaton is actually marginally stable. When the moduli other than the dilaton is stabilized at the self-dual point, the potential for the dilaton disappears and then the dilaton is stabilized due to the Hubble damping. In order to investigate if this mechanism works in more general cases, we analyze the stability of $T_2\otimes T_2\otimes T_2$ compactification in the context of massless string gas cosmology. We found that the volume moduli, the shape moduli, and the flux moduli are stabilized at the self-dual point in the moduli space. Thus, it is proved that this simple compactification model is stable.

Compact binaries consisting of neutron stars/black holes on eccentric orbit undergo a perturbed Keplerian motion. The perturbations are either of relativistic origin or are related to the spin, mass quadrupole, and magnetic dipole moments of the binary components. The post-Newtonian motion of such systems decouples into radial and angular parts. We present here for the first time the radial motion of such a binary encoded in a generalized Kepler equation, with the inclusion of all above-mentioned contributions, up to linear order in the perturbations. Together with suitably introduced parametrizations, the radial motion is solved completely.

We propose an alternative formalism to simulate cosmic microwave background (CMB) temperature maps in $\Lambda \mathrm{CDM}$ universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial sections. Instead, the covariance matrix of the coefficients of the spherical harmonic decomposition of the temperature anisotropies is expressed in terms of the elements of the covering group of the space. We obtain a decomposition of the correlation matrix that isolates the topological contribution to the CMB temperature anisotropies out of the simply connected contribution. A further decomposition of the topological signature of the correlation matrix for an arbitrary topology allows us to compute it in terms of correlation matrices corresponding to simpler topologies, for which closed quadrature formulas might be derived. We also use this decomposition to show that CMB temperature maps of (not too large) multiply connected universes must show “patterns of alignment,” and propose a method to look for these patterns, thus opening the door to the development of new methods for detecting the topology of our Universe even when the injectivity radius of space is slightly larger than the radius of the last scattering surface. We illustrate all these features with the simplest examples, those of flat homogeneous manifolds, i.e., tori, with special attention given to the cylinder, i.e., $T^1$ topology.

Evidence from the Wilkinson Microwave Anisotropy Probe (WMAP) polarization data indicates that the Universe may have been reionized at very high redshift. It is often suggested that the ionizing UV flux originates from an early population of massive or very massive stars. Depending on their mass, such stars can explode either as type II supernovae or pair-instability supernovae, or may entirely collapse into a black hole. The resulting neutrino emission can be quite different in each case. We consider here the relic neutrino background produced by an early burst of Population III stars coupled with a normal mode of star formation at lower redshift. The computation is performed in the framework of hierarchical structure formation and is based on cosmic star formation histories constrained to reproduce the observed star formation rate at redshift $z\lesssim 6$, the observed chemical abundances in damped Lyman alpha absorbers and in the intergalactic medium, and to allow for an early reionization of the Universe at $z\sim 10-20$. We find that although the high redshift burst of Population III stars does lead to an appreciable flux of neutrinos at relatively low energy ($E_{\nu }\approx 1\mathrm{MeV}$), the observable neutrino flux is dominated by the normal mode of star formation. We also find that predicted fluxes are at the present level of the SuperK limit. As a consequence, the supernova relic neutrino background has a direct impact on models of chemical evolution and/or supernova dynamics.

We obtain the effective inflaton potential during slow-roll inflation by including the one-loop quantum corrections to the energy momentum tensor from scalar curvature and tensor perturbations as well as from light scalars and Dirac fermions coupled to the inflaton. During slow-roll inflation there is an unambiguous separation between super- and subhorizon contributions to the energy momentum tensor. The superhorizon part is determined by the curvature perturbations and scalar field fluctuations: both feature infrared enhancements as the inverse of a combination of slow-roll parameters which measure the departure from scale invariance in each case. Fermions and gravitons do not exhibit infrared divergences. The subhorizon part is completely specified by the trace anomaly of the fields with different spins and is solely determined by the space-time geometry. The one-loop corrections to the amplitude of curvature and tensor perturbations are obtained to leading order in slow roll and in the $(H/M_{\mathrm{Pl}}{)}^2$ expansion. A complete assessment of the backreaction problem up to one loop including bosons and fermions is provided. The result validates the effective field theory description of inflation and confirms the robustness of the inflationary paradigm to quantum fluctuations. Quantum corrections to the power spectra are expressed in terms of the CMB observables: $n_s$, $r$ and $d{n}_s/d\ln k$. Trace anomalies (especially the graviton part) dominate these quantum corrections in a definite direction: they enhance the scalar curvature fluctuations and reduce the tensor fluctuations.

We perform a wide parameter-space search for continuous gravitational waves over the whole sky and over a large range of values of the frequency and the first spin-down parameter. Our search method is based on the Hough transform, which is a semicoherent, computationally efficient, and robust pattern recognition technique. We apply this technique to data from the second science run of the LIGO detectors and our final results are all-sky upper limits on the strength of gravitational waves emitted by unknown isolated spinning neutron stars on a set of narrow frequency bands in the range $200–400\mathrm{Hz}$. The best upper limit on the gravitational-wave strain amplitude that we obtain in this frequency range is $4.43\times {10}^{-23}$.

We investigate the point-parity and mirror-parity handedness of the large angle anisotropy in the cosmic microwave background (CMB). In particular we consider whether the observed low CMB quadrupole could more generally signal odd point-parity, i.e., suppression of even multipoles. Even though this feature is “visually” present in most renditions of the WMAP dataset we find that it never supports parity preference beyond the meagre $95\%$ confidence level. This is fortunate as point-parity handedness implies almost certainly a high level of galactic contamination. Mirror reflection parity, on the contrary, is related to the emergence of a preferred axis, defining the symmetry plane. We use this technique to make contact with recent claims for an anisotropic Universe, showing that the detected preferred axis is associated with positive (even) mirror parity. This feature may be an important clue in identifying the culprit for this unexpected signal.

We study the exact (one-loop) effective potential of the littlest Higgs model and determine the dependence of physical quantities, such as the vacuum expectation value $v_W$ and mass $m_h$ of the Higgs boson, on the fundamental parameters of the Lagrangian—masses, couplings of new states, the fundamental scale $f$ of the sigma model, and the coefficients of operators quadratically sensitive to the cutoff of the theory. On the one hand, we show that it is possible to have the electroweak ground state and a relatively large cutoff $\Lambda =4\pi f$ with $f$ in the 2 TeV range without requiring unnaturally small coefficients for quadratically divergent quantities, and with only moderate cancellations between the contribution of different sectors to the effective potential of the Higgs. On the other hand, this cannot be achieved while at the same time keeping $m_h$ close to its current lower bound of 114.4 GeV. The natural expectation for $m_h$ is $O(f)$, mainly because of large logarithmically divergent contributions to the effective potential of the top-quark sector. Even a fine-tuning at the level of $O({10}^{-2})$ in the coefficients of the quadratic divergences is not enough to produce small physical Higgs masses, and the natural expectation is in the 800 GeV range for $f\sim 2\mathrm{TeV}$. We conclude that the littlest Higgs model is a solution of the little hierarchy problem, in the sense that it stabilizes the electroweak symmetry breaking scale to be a factor of 100 less than the cutoff of the theory, but this requires a quite large physical mass for the Higgs, and hence precision electroweak studies should be redone accordingly. We also study finite temperature corrections. The first order electroweak phase transition is no stronger than in the standard model. A second phase transition (nonrestoration of symmetry at high temperature) depends strongly on the logarithmic terms in the potential.